Method and apparatus for solar panel tracking

ABSTRACT

A method for tracking the movement of the sun from East to West across the sky during daylight hours to enable solar photovoltaic (PV) panels or arrays of such panels to capture significantly more solar energy than fixed solar panels. Readily-available sun position data (taken from ephemeris or celestial navigation tables) can be programmed into read-only memory (ROM) chips. Date and time of day information can also be programmed into ROM chips powered by long-life, rechargeable batteries, such as lithium-ion batteries. Using such ROM chip data, a solar panel or an array of solar panels can track the sun position provided that during installation (with the panels aimed longitudinally towards the South), the solar panels are positioned upwards towards the noontime sun position to establish a starting point. This enables the sun tracking system of the present invention to track the sun without requiring a solar sensing device. Sun tracking provides an increase of from about 20% to 50% increased solar energy capture compared with fixed, non-tracking solar panels. Experimental data is also provided to illustrate the effectiveness of the present invention.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from provisional application No.60/555,694 filed Mar. 24, 2004, which is incorporated herein in itsentirety by this reference.

FIELD OF THE INVENTION

The present invention relates to tracking the movement of the sun fromEast to West across the sky during daylight hours to enable solarphotovoltaic (PV) panels, or arrays of such panels to capturesignificantly more solar energy than fixed solar panels.Readily-available sun position data (taken from ephemeris or celestialnavigation tables) can be programmed into read-only memory (ROM) chips.Date and time of day information can also be programmed into ROM chipspowered by long-life, rechargeable batteries, such as lithium-ionbatteries. Using such ROM chip data, a solar panel or an array of solarpanels can track the sun position provided that during installation(with the panels aimed longitudinally towards the South), the solarpanels are positioned upwards towards the noontime sun position toestablish a starting point. This enables the sun tracking system of thepresent invention to track the sun without requiring a solar sensingdevice. Sun tracking provides an increase of from about 20% to 50%increased solar energy capture compared with fixed, non-tracking solarpanels. Experimental data is also provided to illustrate theeffectiveness of the present invention.

BACKGROUND OF THE INVENTION

Solar photovoltaic (PV) panel systems are becoming increasinglyimportant for residential or commercial energy supply, due to theincreasing cost of conventional grid-supplied electricity and the desireto reduce environmental pollution as well as utilize renewable sourcesof energy. In recent years, improved production and designs have reducedthe cost of solar PV panels and related storage battery and electricpower inverter equipment. However, large flat “billboard” sized solarpanels are both unattractive for residential purposes and also requireexpensive structural mounting equipment, especially in high wind loadingareas. One method to reduce the size of solar panels is to provide suntracking, because a solar panel that can track the movement of the sunacross the daytime sky can capture from about 20% to about 50% increasedsolar energy compared with a fixed, non-tracking solar panel. Therefore,for the same energy capture, a tracking-type of solar panel can be 20%to 50% smaller and therefore less expensive and more practical comparedwith a fixed, non-tracking solar panel.

Several types of sun tracking systems are commercially available. Onetype uses a sun sensor with at least two photocells, one pointed Eastand the other pointed West. With this system, sun tracking can beaccomplished by moving the solar panel to equalize the East and Westphotocell sensor readings. Another type uses a fluid inside relativelylarge solar energy collector tubes mounted on the East and West sides ofthe solar panel. With this system, the working fluid inside the tubesexpands as it becomes warmed from solar energy. Sun tracking isaccomplished by moving the solar panel to equalize the amount ofexpansion inside each of the two tubes. In both such systems, arelatively large solar panel is rotated from East (at sunrise) to West(at sunset) with the longitudinal axis of the solar panel facing Southat solar noon when the sun is at its highest elevation angle withrespect to the horizon. Both such systems suffer the disadvantages of(a) poor sun tracking performance caused by dirt, bird droppings, orother material that might collect on the photocell sensors or thecollector tubes, and (b) relatively expensive structural membersdesigned to provide the necessary rotating capability for a relativelylarge flat solar panel array, generally at least about 4×6 feet in size,but perhaps as much as 12×18 feet in size.

The objective of the present invention is to provide a means of suntracking to reduce the cost and size of tracking-type solar panelsystems, without requiring the use of photocell sensors or collectingtubes, and also to provide sun tracking with a low-profile solar arrayconfiguration that would not be aesthetically unpleasing andobjectionable for use in residential areas.

BRIEF DESCRIPTION OF THE INVENTION

The present invention does not require the use of any type of solarsensing photocell or thermal collecting tube device to enable a solarpanel (or array of solar panels) to track the sun. The present inventionmakes use of readily-available sun position data (taken from ephemerisor celestial navigation tables). These data are programmed intoread-only memory (ROM) chips. Date and time of day information are alsoprogrammed into ROM chips powered by long-life, rechargeable batteries,such as lithium-ion batteries, similar to the ROM chips used in personalcomputers which provide day, date and clock time for computer users.Using such ROM chip data, a solar panel or an array of solar panels cantrack the sun position provided that during installation (with thepanels aimed with the longitudinal axis pointed towards the South), atleast one time versus position point is established as a starting point.One such easily-established point is to position the one or more solarpanels aimed straight upwards when the sun reaches its highest zenithpoint at solar noon. The system of the present invention then receivesan input signal to establish this initial starting point. The trackingsystem of the present invention is then energized to become fullyoperational.

Because of differences in sun position with respect to the horizon atdifferent geographical latitude locations on the earth, it is alsodesirable to provide a second solar panel position starting point input,which can be used to improve and refine the tracking ability becauseadjustments programmed within the ROM chip can be set up to account forlatitude locations if a second input is provided. For example, anothersuch input signal can be established by aiming the solar panels directlytowards the sun at some other known time which is several hoursdifferent from solar noon. Once at least two such points areestablished, the sun tracking system of the present invention enablesthe solar panels to track the sun with improved accuracy whichcompensates for different geographic latitude locations.

Another feature of the present invention is to provide a verylow-profile solar panel array which lies flat with the surface of almostany type of roof or structure. This eliminates the need to have large“billboard” size solar panels which are aesthetically unpleasing andobjectionable for use in most residential areas. The physical appearanceof such solar panel arrays would be much more acceptable for use inresidential applications, because they would appear to be roof vents,skylights, or louvers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a line drawing showing the arrangement of the experimentalsystem used for testing the present invention which illustrates theconfiguration of the basic components, in this case being three solarpanels. In practice, these solar panels are preferably operated inunison by means of a captive rack and pinion gear arrangement driven bya reversible DC gearmotor, the gearmotor being controlled by inputsprovided from the ROM chips and the control circuit;

FIG. 2 is a dimensional drawing showing the arrangement of a typicalsolar module array of the present invention;

FIG. 3 shows the effect of adjacent solar panel spacing on the amount ofsolar energy blockage incurred at low sun angles when the sun in lowtowards the horizon;

FIG. 4 depicts the position of the sun versus time of day, and when usedwith the explanations in the specification text, enables betterunderstanding of the method used to determine sun position, and hence,the required solar panel tracking angle;

FIG. 5 is a graph showing the decrease in solar energy capture for atypical solar panel when the sun angle deviates away from beingperpendicular to the solar panel surface, thus illustrating theimportance of tracking the sun to keep the sun angle as close toperpendicular to the solar panel surface as possible as the sun movesacross the sky from East to West;

FIG. 6 is a graphical depiction of the improvement in solar energycapture comparing tracking versus fixed solar panels mounted on a flathorizontal roof in San Diego, Calif. for the worst case condition atwinter solstice;

FIG. 7 is a graphical depiction of the improvement in solar energycapture comparing tracking versus fixed solar panels mounted on astandard 5/12 roof in San Diego, Calif. for the worst case condition atwinter solstice.

RESULTS OF EXPERIMENTAL TESTING

An experimental solar panel system was constructed to test theeffectiveness of the present invention. A schematic diagram of theexperimental system is shown in FIG. 1, where the components consistedof three (3) rectangular solar panels, 12 a, 12 b and 12 c, eachrotating about a longitudinal axis, 13, and supported by a framework,11. For the purposes of these experiments, the solar panels weremanually rotated during data collection. A preferred embodiment of theframework would include a captive rack and pinion gear arrangementdriven by a reversible DC gearmotor, so the solar panels could berotated in unison and kept at the same angle with respect to the sunsimply by suitable inputs provided to the gearmotor.

Results of experimental testing are shown in Table 1, where solar panelelectrical output was passed through a simulated load consisting of asuitable resistor. The voltage across the resistor was measured andaveraged over two independent runs, to enable the power output from thesolar panel to be calculated. The power output in watts is the measuredvoltage squared, divided by the resistance in ohms. The solar panelswere aimed with the long axis pointing directly East to allow the effectof changing sun angle to be measured over a short period of time as thesolar panels were manually rotated from one angle to the next. Thesetests were conducted at noon on Oct. 17, 2003 in San Luis Obispo, Calif.with blue sky conditions. The voltages across the resistor were measuredand recorded for various sun angles with respect to the solar panelsurface. The results were then transposed to calculate the power outputfrom the solar panel assuming a 12 hour day, first with a fixed solarpanel and second, assuming that the solar panels were enabled to trackthe sun. The solar energy capture with sun tracking was about 48% morethan provided by the same solar panels in a fixed position to providemaximum solar energy capture at solar noon. The fixed solar panelsprovided less energy capture at all other times of the day, becausefixed panels cannot track the movement of the sun.

Based on these experimental tests, it was obvious that significantimprovements in solar energy capture could be obtained with a lowprofile solar tracking module according to the present invention.

TABLE 1 Solar Panel Tracking Tests Tracking Solar Panel Fixed PanelPanel Measured Calculated Fixed Tracking Angle Sun Hours Sun HoursVoltage Watts Watt-Hours Watt-Hours 90.00 1.50 12.00 3.22 2.254 3.38127.048 78.75 1.50 n/a 3.22 2.254 3.381 67.50 1.50 n/a 3.05 2.022 3.03356.25 1.50 n/a 2.98 1.931 2.896 45.00 1.50 n/a 2.76 1.656 2.484 33.751.50 n/a 2.24 1.091 1.636 22.50 1.50 n/a 1.78 0.689 1.033 11.25 1.50 n/a1.20 0.313 0.470 0.00 0.00 n/a 0.61 0.081 0.000 Totals 18.314 27.048Rotate Percent Improvement over Fixed Baseline 47.7% Test Date: Oct. 17,2003 at 12:00 Noon in San Luis Obispo, CA 93401, blue sky conditionsNOTES: 1. Watts = (volts)*(volts)/(ohms) where ohms = 4.6 ohms (5 wattresistor) 2. Solar panel: 2 rows of 12 silicon crystal cells @ 1 × 2inches each, total 48 sq. in. 3. Panel substrate: FRP with Tefzel overthe silicon crystal cells 4. Voltages averaged over two independent runswith stable resistor temperature

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

As already shown in FIG. 1, the preferred embodiment for solar panelarrays of the present invention is to arrange long rectangular solarpanels in an array like a shutter or a Venetian blind, with thelongitudinal axis, 13, of the solar panels, 12 a, 12 b and 12 c, to beaimed directly South, and being enabled to rotate about the longitudinalaxis from East to West during daylight hours to thereby track themovement of the sun.

A diagram of such a sun tracking module is shown in FIG. 2, whichprovides one preferred embodiment of the present invention. As shown inFIG. 2, there are 9 solar panels, 20 a through 20 i, arranged in amodular frame, 21, with outside dimensions of 24 by 48 inches, i.e. 2×4feet, which fits with most of the roof framing dimensions used in theUnited States. Each solar panel is approximately 4.3 inches wide by 21.8inches long, and contains 30 solar PV cells connected in series, eachcell about 4.0×0.7 inches in size, with a total of about 84 sq.in. ofactive cell surface area. This solar module with 9 such rotating solarpanels contains about 756 sq. in. of active cell area, and will produceabout 14 VDC at about 4.5 amperes, maximum of about 63 watts ofelectrical power in full sunlight with the solar array pointed directlytowards the sun. The active cell area is about 66% of the total areabased on the outside dimensions of the modular frame. The full sunlightopen circuit voltage for such a solar panel array would be more like17.8 VDC, but in actual practice, the working voltage for purposes ofrating the power output from a solar module is decreased about 20%.

One preferred method for rotating all the sun tracking solar panels inunison is to use a captive rack and pinion gear mechanism, 22 a and 22b, with pinion gears, 22 b, mounted on each of the axial shafts, 23,connected to each of the parallel-mounted solar panels, 20 a through 20i, with each axial shaft, 23, securely mounted in a suitable bearing onthe solar module framework, 21. The linear rack gear, 22 a, is thenpreferably supported and “captured” by suitably-flanged roller bearings,which are also mounted on the same solar module framework, 21. East toWest sun tracking movement of all the solar panels in unison can then beaccomplished using a suitable reversible actuator. For example, acaptive-nut type of linear actuator motor could be used, such as the 12VDC automobile car antenna actuator motor. Other similar types ofactuators could be used, such as a reversible DC gearbox motor, 24, witha pinion driving gear that operates both back and forth to move thetoothed rack gear, 22 a, over a desired linear distance. The type ofactuator itself is not critical, except that it must be capable of bothpushing and pulling the linear rack gear, 22 a, so that after suntracking all day long until evening, then, after sunset in the West, thesolar panel array can be returned to the East sunrise position, to beready for another day of sun tracking at sunrise. As previously stated,the time of day signals needed to enable the control system to know whensunset occurs and when to return the solar panels towards the East toanticipate sunrise on the next day comes from a suitable ROM chip. TheROM chip can be powered from a small long-lifetime battery locatedinside the control system, or from energy storage batteries that areused for storing the solar energy captured by the solar panel system.

It is preferred that the solar panels are capable of rotating at leastabout +/−60 degrees from being flat (or pointed straight upwards) withrespect to the solar module framework, 21. The pinion gears, 22 b, oneach of the solar panel longitudinal axes, 23, are preferably formed ashalf-circles, to avoid having any portion of the pinion gear itselfprojecting upwards beyond the plane of the solar panels, and therebykeeping a low profile and also avoiding any sun blockage that wouldreduce solar energy capture.

The sun tracking solar module of the present invention can be installedon any type of roof, gazebo, greenhouse, patio, open ground, or almostany other type of preferred structure, and not limited to the roof of aresidential home or commercial office building. The external physicalappearance of the sun tracking solar module of the present invention issimilar to a roof vent or louver, and could also be mistaken for sometype of skylight. One preferred embodiment, especially for severe winterweather conditions with snow and ice, is to enclose the sun trackingsolar module of the present invention inside a flat skylight ordome-shaped transparent or translucent housing designed to minimize theamount of solar energy lost because of sunlight transmission through thehousing towards the solar panels. One preferred embodiment is a flatglass covering over the top surface of the module framework, elevatedsufficiently to allow free rotation of the solar panels which would beprotected inside. The overall height of such a flat glass-covered modulefor the preferred embodiment of FIG. 2 would be about 5 inches—veryacceptable for most residential installations. It should also be notedthat such a “skylight” configuration would actually function rather wellas a skylight, blocking most of the direct sunlight, but allowingindirect light transmission from the blue sky to pass through the planeof the solar module for interior lighting purposes, as might be desired.

One disadvantage of the preferred linear array of parallel solar panelsis that when the sun elevation angle with respect to the horizon is low,each solar panel tends to shade, or block, the adjacent solar panel.This effect for the 4.3 inch wide solar panels mounted on 5.0 inchcenters is shown in FIG. 3, where the sun elevation angles correspondingto various amounts of blockage are calculated. For example, if the sunelevation angle is about 20 degrees, there would be a blockage factor ofabout 50%. The percentage open area between adjacent solar panels inFIG. 3 is about 14%. If the percentage open area is increased, there isless blockage for a given sun elevation angle. For example, if the openarea is increased to about 33% (4.3 inch wide solar panels on 6.5 inchcenters), the solar blockages versus sun elevation angles change asfollows:

14% Open Area 33% Open Area  0% Blocked 47.6 deg.  0% Blocked 38.5 deg.Sun Angle Sun Angle 25% Blocked 34.9 deg. 25% Blocked 26.6 deg. SunAngle Sun Angle 50% Blocked 20.8 deg. 50% Blocked 16.7 deg. Sun AngleSun Angle 75% Blocked 9.0 deg. 75% Blocked 8.4 deg. Sun Angle Sun Angle

Therefore, by suitable selection of percentage open area, the amount ofblockage can be adjusted as may be desired.

Calculating Sun Position Vs. Time of Day

The position of the sun as determined from typical locations in theUnited States can be described in terms of sun azimuth angle (i.e.looking downwards on the horizontal plane and determining the sunposition with respect to the four directions of the compass) and the sunelevation angle above the horizon. Since the earth is spherically shapedand revolves on its axis at a constant speed, and since the earthrotates around the sun in a circular orbit, it is possible to exactlypredict the position of the sun from any given point on the surface ofthe earth as a function of the time of day. Sun position data can beobtained from published celestial navigation tables or ephemeris tables.One very convenient source of such data is found on the InterNet. It isposted by the California Institute of Technology Jet PropulsionLaboratory, and is called the JPL Horizons Ephemeris Generator. It canbe found on the InterNet at URL: http://ssd.jpl.nasa.gov/cgi-bin/eph

Tables 4 and 5 (below) provide examples of the data for the winter andsummer solstices at San Diego, Calif., which were obtained using the JPLHorizons Ephemeris Generator. Note that at San Diego, the sun elevationangle with respect to the horizon at solar noon changes from 33.8degrees on the winter solstice to 80.7 degrees on the summer solstice.Since the short winter days with lower sun angle represent the worstcase conditions for solar energy capture, the calculations which followare based on the winter solstice data and information.

TABLE 4 Winter Solstice San Diego, CA Ephemeris Generator EphemerisSettings Target Body: Sun (Sol) Observer Location: San Diego, CACoordinates: 117° 09′21.6′′W, 32° 42′52.9′′N From: A.D. 2003-12-20 00:00UT-8 (PST) To: A.D. 2003-12-25 00:00 Step: 1 minute, Rise/Transit/Setonly (TVH) Format: Calendar Date and Time Output Quantities: 2, 4 Ref.Frame, RA/Dec Format: J2000, HMS Apparent Coordinates Model: AirlossHORIZONS Generated Ephemeris Ephemeris/WWW_USER Mon Mar 22 08:52:42 2004Pasadena, USA/Horizons Target body name: Sun (10) {source:DE-0406LE-0406} Center body name: Earth (399) {source: DE-0406LE-0406}Center-site name: (User Defined Site) Start time: A.D. 2003-Dec-2000:00:00.0000 UT-08:00 Stop time: A.D. 2003-Dec-25 00:00:00.0000UT-08:00 Step-size: 1 minutes Center geodetic: 242.844000, 32.7147,−0.00 {E-lon(deg), Lat(deg), Alt(km)} Center cylindric: 242.844000,5371.6412, 3427.38 {E-lon(deg), Dxy(km), Dz(km)} Center pole/equ:High-precision EOP model {East-longitude +} Center radii: 6378.1 ×6378.1 × 6356.8 km {Equator, meridian, pole} Target pole/equ: IAU_SUN{East-longitude +} Target radii: 696000.0 × 696000.0 × 696000.0 k{Equator, meridian, pole} Target primary: Sun {source: DE-0406LE-0406}Interfering body: MOON (Req = 1737.400) km {source: DE-0406LE-0406}Deflecting body: Sun, EARTH {source: DE-0406LE-0406} Deflecting GMs:1.3271E+11, 3.9860E+05 km{circumflex over ( )}3/s{circumflex over ( )}2Atmos refraction: NO (AIRLESS) RA format: HMS Time format: CAL Timezone: UT-08:00 RTS-only print: TVH RTS elevation: 0. degrees EOP file:eop.040319.p040610 EOP coverage: DATA-BASED 1962-JAN-20 TO 2004-MAR-19.PREDICTS−> 2004-JUN-09 Units conversion: 1 AU = 149597870.691 km, c =299792.458 km/s, 1 day = 86400.0 s Date_(ZONE)_HR:MNR.A._(a-apparent)_DEC Azi_(a-appr)_Elev 2003-Dec-20 06:47 Cr 17 52 33.31−23 25 50.3 117.7005 −0.6951 2003-Dec-20 11:47 *t 17 53 28.29 −23 2601.9 180.2259 33.8511 2003-Dec-20 16:47 Cs 17 54 23.26 −23 26 07.9242.5143 −1.0029 2003-Dec-21 06:47 Cr 17 56 59.75 −23 26 23.7 117.6413−0.7933 2003-Dec-21 11:47 *t 17 57 54.75 −23 26 29.4 180.0882 33.8437 ←33.8° 2003-Dec-21 16:47 Cs 17 58 49.73 −23 26 29.5 242.4428 −0.91342003-Dec-22 06:48 Cr 18 01 26.45 −23 26 28.9 117.7095 −0.7009

TABLE 5 Summer Solstice San Diego, CA Ephemeris Generator EphemerisSettings Target Body: Sun (Sol) Observer Location: San Diego, CACoordinates: 117° 09′21.6′ ′W, 32° 42′52.9′′N From: A.D. 2003-06-2000:00 UT-8 (PST) To: A.D. 2003-06-25 00:00 Step: 1 minute,Rise/Transit/Set only (TVH) Format: Calendar Date and Time OutputQuantities: 2, 4 Ref. Frame, RA/Dec Format: J2000, HMS ApparentCoordinates Model: Airloss HORIZONS Generated EphemerisEphemeris/WWW_USER Mon Mar 22 08:50:47 2004 Pasadena, USA/HorizonsTarget body name: Sun (10) {source: DE-0406LE-0406} Center body name:Earth (399) {source: DE-0406LE-0406} Center-site name: (User DefinedSite) Start time: A.D. 2003-Jun-20 00:00:00.0000 UT-08:00 Stop time:A.D. 2003-Jun-25 00:00:00.0000 UT-08:00 Step-size: 1 minutes Centergeodetic: 242.844000, 32.7147,- −0.00 {E-lon(deg), Lat(deg), Alt(km)}Center cylindric: 242.844000, 5371.6412, 3427.38 {E-lon(deg), Dxy(km),Dz(km)} Center pole/equ: High-precision EOP model {East-longitude +}Center radii: 6378.1 × 6378.1 × 6356.8 km {Equator, meridian, pole}Target pole/equ: IAU_SUN {East-longitude +} Target radii: 696000.0 ×696000.0 × 696000.0 k {Equator, meridian, pole} Target primary: Sun{source: DE-0406LE-0406} Interfering body: MOON (Req = 1737.400) km{source: DE-0406LE-0406} Deflecting body: Sun, EARTH {source:DE-0406LE-0406} Deflecting GMs: 1.3271E+11, 3.9860E+05 km{circumflexover ( )}3/g{circumflex over ( )}2 Atmos refraction: NO (AIRLESS) RAformat: HMS Time format: CAL Time zone: UT-08:00 RTS-only print: TVH RTSelevation: 0. degrees EOP file: eop.040319.p040610 EOP coverage:DATA-BASED 1962-JAN-20 TO 2004-MAR-19. PREDICTS−> 2004-JUN-09 Unitsconversion: 1 AU = 149597870.691 km, c = 29979 2.458 km/s, 1 day =86400.0 s Date_(ZONE)_HR:MN R.A._(a-apparent)_DEC Azi_(a-appr)_Elev2003-Jun-20 04:41 Cr 05 54 43.39 +23 25 58.3 61.1912 −0.8196 2003-Jun-2011:51 *t 05 55 57.44 +23 26 10.5 181.2062 80.7196 2003-Jun-20 19:00 Cs05 57 11.27 +23 26 12.9 298.9073 −0.9456 2003-Jun-21 04:42 Cr 05 5853.16 +23 26 17.5 61.2937 −0.6722 2003-Jun-21 11:51 *t 06 00 07.04 +2326 22.3 180.8972 80.7237 ← 80.7° 2003-Jun-21 19:00 Cs 06 01 20.87 +23 2617.3 298.8785 −0.9048 2003-Jun-22 04:22 Cr 06 03 02.76 +23 26 11.961.2653 −0.7132

The length of the day at various longitude locations along the WestCoast of the United States were determined from the same JPL Horizonsprogram. For example, on the shortest day of the year, the wintersolstice, the following information was obtained:

Location Latitude Sunrise Sunset Length of Day San Diego, CA 32 deg N06:47 16:47 10 hr 0 min Eugene, OR 44 deg N 07:48 16:43 8 hr 55 minSeattle, WA 47 deg N 07:58 16:27 8 hr 09 min Bellingham, WA 48 deg N08:03 16:23 8 hr 03 min

It is thus seen that the length of day at winter solstice varies byabout 2 hours on December 21 for locations varying from the USA borderwith Canada on the North and the USA border with Mexico on the South. Ifan intermediate location were selected as being representative of theentire USA, such as 40 degrees North latitude, then the sunriseprediction on the winter solstice would be about 07:25 hours. Thisprediction would be 38 minutes behind the actual sunrise time in SanDiego, Calif. and 38 minutes before the actual sunrise time inBellingham, Wash. However, the time of solar noon would be just aboutthe same for all the various locations up and down the West Coast of theUnited States. The maximum error of 38 minutes occurs only at sunriseand sunset, where there is very little solar energy capture, anddecreases as the sun approaches solar noon. The length of day estimateerror increasing again as the sun sets, at which time there is verylittle solar energy capture available.

Careful experiments were conducted to determine the loss of solar energycapture as a function of the angle of the sun with respect to the placeof the solar panel. As shown in FIG. 5, the loss in solar energy captureby a solar panel is less than about 11% so long as the angle of the sunto the solar panel is 60 degrees or greater, with 90 degrees beingperfect. A maximum error of 38 minutes in solar panel tracking positionamounts to an error of 9.5 degrees in solar panel tracking angle,representing a maximum loss of about 2% in solar energy capture, asdetermined from FIG. 5. This is considered to be an acceptable source ofinaccuracy in the preferred solar tracking method of the presentinvention. Therefore, a simplified solar tracking model can be developedwhich will function adequately for all locations in the United States,from the Northern border to the Southern border. However, for any givenlocation, adjustments need to be made for the longitudinal location(i.e. time of day) as well as the mounting angle of the sun trackingmodule, whether on a flat roof, or a roof with a given pitch angle, aswill be discussed further below. The key point, however, is that apractical sun tracking system can operate successfully in a variety ofgeographic locations, without requiring the use of any type of solarsensor, such as a photocell system, or thermal sensor, such as acollector tube system.

The JPL Horizons Ephemeris Generator provides the sun elevation angle atsolar noon, as well as the times and sun azimuth angles at both sunriseand sunset. Given this information, it is relatively straightforward todetermine the sun position at any time of day. For simplicity, thesecalculations were performed graphically as shown in FIG. 4.

FIG. 4 shows the winter solstice sun positions versus time of day forSan Diego, Calif. The upper unit circle represents the sun azimuthangles versus time of day, looking downwards on the four directions ofthe compass. From Table 4, at sunrise, 06:47, the sun azimuth angle is117.7. Subtracting 90 degrees, the sun offset angle from the East-Westdirection is shown in FIG. 4 as 27.7 degrees at sunrise. From Table 4,we also know the length of the day (10 hours 0 minutes) and the time ofsunset as well as the time at solar noon, or mid-day. Since the earthrotates at constant speed, the progression of sun offset angle versushours in the day are shown marked off in the upper unit circle of FIG.4. Each hour, the sun offset angle increases by 12.46 degrees (i.e. 62.3divided by 5). Therefore, the sun offset angle at the 2^(nd) hour aftersunrise is 52.6 degrees.

The lower unit circle in FIG. 4 represents the sun elevation anglesversus time of day, with the position of the horizon for the wintersolstice day in San Diego marked as shown. Fortunately, the suntraverses a circular arc across the sky, not an elliptical or aparabolic arc. Once the sun elevation angle of 33.8 degrees at solarnoon is determined (i.e. from Table 4), then the position of the horizonon the unit circle can be drawn at a distance (corresponding to the sineof the sun elevation angle) below the mid-day position on the unitcircle.

The sun azimuth angles for the daylight hours are shown in the upperunit circle. These correspond directly with the sun elevation angles forthe daylight hours in the lower unit circle. The connections betweenthese two sun position indicators are shown in dotted lines in FIG. 4.The sun elevation angles for the daylight hours are then determined bymeasuring the height above the horizon and calculating the arc sin ofthe measured height (divided by 1 for a unit circle). For example, atthe 2^(nd) hour after sunrise, the height of the sun above the horizonline is measured to be 0.347 vertically upwards to the arc of the unitcircle, and the arc sin of 0.347 is 20.3 degrees, which is the sunelevation angle at the 2^(nd) hour after sunrise. Similar calculationscan be made for this particular location and date as shown in Tables 2and 3.

Table 2 provides a comparison of the mA current capture during thedaylight hours for fixed vs. tracking solar panels located on a flathorizontal roof located in San Diego, Calif. on December 21 or thewinter solstice. Table 3 provides the same comparison for solar panelslocated on a standard 5/12 pitch roof in the same location on the sameday. A somewhat complex physical model was constructed to enable directmeasurement of the sun angle with respect to the plane of the solarpanel. This physical model used string to represent the sunlight rays,and the string was set at the given sun elevation angle above a flathorizontal surface. Next, the position of the solar panel array wasadjusted to be at the correct angle with respect to the string torepresent the correct sun offset angle (sun azimuth angle). For thefixed solar panel, the angle of the string (representing the rays ofsunlight) measured perpendicular to the plane of the solar panel wasdetermined. For the easiest situation, Case 1 with the solar panelmounted on a flat horizontal roof, the sun angles to the fixed panelwere the same as the sun elevation angles. Then, using FIG. 5 again, thepercentage of maximum current output could easily be determined. For thesun tracking module, the best solar panel rotation angle for maximizingthe sun angle to panel were decided experimentally, and the resultsalong with the percentage of maximum current output were again recorded.As shown in Table 2 (on the next page), the rotating solar panelscapture 62% more mA current than the fixed solar panel for Case 1 on aflat roof in San Diego, Calif. on December 21 or the winter solstice.

Similar experiments and calculations were conducted for Case 2, with thetwo types of solar panel on a standard 5/12 pitch roof in San Diego,Calif. on December 21 or winter solstice. As shown in Table 3 (on thefollowing page), the rotating solar panels capture 20% more mA currentthan the fixed solar panel.

TABLE 2 Case 1 Data - Flat Roof SunTracker Solar Panel Tracking SystemCalculation of Improved Performance vs. Fixed Solar Panel Mar. 22, 2004,DG Jones, Panel Location: San Diego, California, USA, 117-deg W, 32-degN Worst Case Winter Soltice Day: Dec 21, 2003 Sun Azimuth Angle: 27.7deg (offset from 90-deg due East) Sun Elevation at Mid-Day: 33.9 deg (asmeasured above horizon plane) Sunrise Time: 0647 hr Mid-Day Time: 1147hr Sunset Time: 1647 hr Length of Day: 10.0 hr Rotating Solar PanelsFacing Due South with +/− 60 degree rotate capability Case 1: SolarPanels positioned parallel with horizon (straight up) Case 2: SolarPanels on standard 5/12 roof, or 22.6 deg tilt above horizontal NOTES:Please see unit circle figures which accompany this chart. Below 20 degsun elevation, partial blockage of rotate panels occurs Partial Blockageestimated at 25% for +1 and +9 hours and 75% for Sunrise and Sunset(Theta) Sin (Theta) Height (h) (Alpha) Case 1 - Panel Flat with HorizonSun Unit Circle Above Unit Sin-1 (h) Sun Angle Fixed Panel Best PanelSun Angle Rotate Panel Azimuth Height Circle Sun to Fixed % of Max.Rotation to Panel % of Max. Hour Offset Above E-W Horizon ElevationPanel Current Angle with Rotate Current Sunrise 27.7 0.465 0.000 0.0 0.08.0% 60 41.0 17.0% “+1” 40.2 0.645 0.182 10.5 10.5 18.0% 60 47.0 57.0%“+2” 52.6 0.794 0.347 20.3 20.3 30.0% 60 42.0 70.0% “+3” 65.1 0.9070.459 27.3 27.3 44.0% 60 38.0 64.0% “+4” 77.5 0.976 0.526 31.7 31.752.0% 50 35.0 58.0% Mid-Day 90.0 1.000 0.558 33.9 33.9 56.0% 0 33.956.0% “+6” 102.5 0.976 0.526 31.7 31.7 52.0% 50 35.0 58.0% “+7” 114.90.907 0.459 27.3 27.3 44.0% 60 38.0 64.0% “+8” 127.4 0.794 0.347 20.320.3 30.0% 60 42.0 70.0% “+9” 139.8 0.645 0.182 10.5 10.5 18.0% 60 47.057.0% Sunset 152.3 0.465 0.000 0.0 0.0 8.0% 60 41.0 17.0% Daily Totals35.2% 57.1% Percentage Increase over Baseline Baseline 62.2%

TABLE 3 Case 2 Data -- 5/12 Pitch Roof SunTracker Solar Panel TrackingSystem Calculation of Improved Performance vs. Fixed Solar Panel Mar.22, 04, DGJones Panel Location: San Diego, California, USA, 117-deg W,32-deg N Worst Case Winter Soltice Day: Dec 21, 2003 Sun Azimuth Angle:27.7 deg (offset from 90-deg due East) Sun Elevation at Mid-Day: 33.9deg (as measured above horizon plane) Sunrise Time: 0647 hr Mid-DayTime: 1147 hr Sunset Time: 1647 hr Length of Day: 10.0 hr Rotating SolarPanels Facing Due South with +/− 60 degree rotate capability Case 1:Solar Panels positioned parallel with horizon (straight up) Case 2:Solar Panels on standard 5/12 roof, or 22.6 deg tilt above horizontalNOTE: Please see unit circle figures which accompany this chart. Below20 deg sun elevation, partial blockage of rotat panels occurs. PartialBlockage estimated at 25% for +1 and +9 hours and 75% for Sunrise andSunset (Theta) Sin (Theta) Height (h) (Alpha) Case 2 - Panel on Standard5/12 Pitch Roof @ 22.6 degrees Sun Unit Circle Above Unit Sin-1 (h) SunAngle Fixed Panel Best Panel Sun Angle Rotate Panel Azimuth HeightCircle Sun to Fixed % of Max. Rotation to Panel % of Max. Hour OffsetAbove E-W Horizon Elevation Panel Current Angle with Rotate CurrentSunrise 27.7 0.465 0.000 0.0 0.0 8.0% 60 64.0 22.8% “+1” 40.2 0.6450.182 10.5 29.0 46.0% 60 75.0 72.8% “+2” 52.6 0.794 0.347 20.3 43.070.0% 45 65.0 92.0% “+3” 65.1 0.907 0.459 27.3 54.0 82.0% 30 62.0 90.0%“+4” 77.5 0.976 0.526 31.7 57.0 86.0% 15 60.0 89.0% Mid-Day 90.0 1.0000.558 33.9 57.0 86.0% 0 57.0 86.0% “+6” 102.5 0.976 0.526 31.7 57.086.0% 15 60.0 89.0% “+7” 114.9 0.907 0.459 27.3 54.0 82.0% 30 62.0 90.0%“+8” 127.4 0.794 0.347 20.3 43.0 70.0% 45 65.0 92.0% “+9” 139.8 0.6450.182 10.5 29.0 46.0% 60 75.0 72.8% Sunset 152.3 0.465 0.000 0.0 0.08.0% 60 64.0 22.8% Daily Totals 66.2% 79.6% Percentage Increase overBaseline Baseline 20.3%

Looking at both Table 2 and Table 3, it is noteworthy that the bestpanel rotation angle is quite different for the flat roof compared withthe standard 5/12 pitch roof. For example, at +3 hours after sunrise,the flat roof installation would still have the best panel rotationangle at 60 degrees, while for the pitched roof, the best panel rotationangle would be reduced to 30 degrees. Therefore, when installing a suntracking solar module of the present invention, it would be necessaryeither to input the roof pitch angle into the programming scheme, or toorient the solar panel array at the best angle towards the sun at someknown time after sunrise, and enter the result into the programmingscheme. The second method is preferred, because using a straight rodattached perpendicular to the solar panel surface, it is quite easy toadjust the panel rotation angle to minimize the length of the shadowfrom the rod, and this corresponds to the best panel rotation angle.Also, it is easy to understand that as the roof pitch increases, theeffectiveness of the fixed panel increases simply due to increased sunangle, while with the same increased roof pitch, the rotating panel canmore easily approach perfectly perpendicular sun angles over a longernumber of daylight hours.

The results for Case 1 and Case 2 are compared directly in Table 6,which shows the effects of rotating the sun tracking solar module of thepresent invention as compared with a fixed solar panel for these twodifferent roof pitch configurations. Both sets of data are for thewinter solstice day in San Diego, Calif., with a total of 10 daylighthours. To complete the solar energy capture calculations (watt-hours),it was further assumed that the solar panel output voltage drops to 70%of maximum when the solar panel output current drops below 50%.

As shown in Table 6 (on the next page), the sun tracking solar modulecollects about 92% more solar energy than the fixed panel on a flat roof(Case 1) and about 25% more on a standard 5/12 pitch roof. Thesetabulated results are further illustrated in FIG. 6 for the flat roofand FIG. 7 for the pitched roof. It is concluded that regardless theroof pitch angle, the sun tracking solar module of the present inventionprovides significantly increased solar energy capture compared with afixed solar panel, whether the number is 25%, 48% or 92%, all of whichdepend on type of roof; geographic location, day of the year, as well asvariable ambient weather conditions.

TABLE 6 Rotate vs. Fixed Solar Performance Rotate vs. Fixed Solar PanelPerformance Mar. 22, 2004, DGJones Panel Location: San Diego,California, USA, 117-deg W, 32-deg. N Worst Case Winter Soltice Day: Dec21, 2003 Please see Case 1 and Case 2 *.xls files for actual data NOTES:When current drops below 50% of maximum, it is assumed that voltagedrops to 70% of maximum. Case 2 - Panel on Std 5/12 Pitch Roof FixedSolar Panel Rotating Solar Panel Module Hours % Max. % Max. % Max. %Max. % Max. % Max. from Current Voltage Wattage Wattage Current VoltageSunrise mA V W W mA V 0  8%  70% 5.6% 16.1% 23%  70% 1 46%  70% 32.2%73.0% 73% 100% 2 70% 100% 70.0% 92.0% 92% 100% 3 83% 100% 83.0% 90.0%90% 100% 4 86% 100% 86.0% 89.0% 89% 100% 5 86% 100% 86.0% 86.0% 86% 100%6 86% 100% 86.0% 89.0% 89% 100% 7 82% 100% 82.0% 90.0% 90% 100% 8 70%100% 70.0% 92.0% 92% 100% 9 46%  70% 32.2% 73.0% 73% 100% 10  8%  70%5.6% 16.1% 23%  70% Totals 63.3% 79.0% Percentage Increased PowerBaseline 24.8% Case 1 - Panel on Flat Horizontal Roof Fixed Solar PanelRotating Solar Panel Module Hours % Max. % Max. % Max. % Max. % Max. %Max. from Current Voltage Wattage Wattage Current Voltage Sunrise mA V WW mA V 0  8% 70% 5.6% 11.9% 17.0%  70% 1 18% 70% 12.6% 57.0% 57.0% 100%2 30% 70% 21.0% 70.0% 70.0% 100% 3 44% 70% 30.8% 64.0% 64.0% 100% 4 52%100%  52.0% 58.0% 58.0% 100% 5 56% 100%  56.0% 56.0% 56.0% 100% 6 52%100%  52.0% 58.0% 58.0% 100% 7 44% 70% 30.8% 64.0% 64.0% 100% 8 30% 70%21.0% 70.0% 70.0% 100% 9 18% 70% 12.6% 57.0% 57.0% 100% 10  8% 70% 5.6%11.9% 1.70%  70% Totals 29.4% 56.6% Percentage Increased Power Baseline92.2%

Initial Sun Tracking System Setup

As already described above, the effect of roof pitch angle can becompensated for by orienting the solar panel array at the best angletowards the sun at some known time after sunrise, and entering theresult into the tracking system programming scheme.

Readily-available sun position data (taken from ephemeris or celestialnavigation tables) can be programmed into read-only memory (ROM) chips.Date and time of day information can also be programmed into ROM chipspowered by long-life, rechargeable batteries, such as lithium-ionbattery. As with other products such as personal computers, the batterywill continue to operate the clock and keep time from the point ofmanufacture until the sun tracking solar module is installed and putinto operation, after which time the battery will be rechargedautomatically from the solar panel energy capture.

Using such ROM chip data, a solar panel or an array of solar panels cantrack the sun position provided that during installation (with thepanels aimed longitudinally towards the South), at least one sunposition versus time of day is entered into the control system. One sucheasily-established point is to position the solar panels flat with themounting structure at solar noon. Solar noon is generally about the noonhour, but differs according to the longitude of the physical location,since some locations are close to a standard time zone and otherlocations are far away from the border of the time zone.

The accuracy of the sun tracking system can be improved if another suchpoint can be established by aiming the solar panels directly towards thesun at some other selected time which is preferably several hoursdifferent from solar noon, such as +3 hours after sunrise. Based on twosuch data points entered into the control system, there is an improvedability to compensate for differences in geographic location. Whetherone or two or additional sun position versus time of day starting pointsare established and entered into the control system, the sun trackingsystem of the present invention enables the solar panels to track thesun without requiring a solar sensing device. With more than a singlestarting point, the control system can provide improved sun trackingaccuracy.

It should also be noted that on severely cloudy or gray sky overcastdays, there is no need for sun tracking because the solar energy captureis primarily due to the overall brightness of the

1-11. (canceled)
 12. A method for tracking the position of the sunduring daylight hours, consisting of a programmed control system whichdrives a suitable reversible electric motor, thereby causing one or morerotating solar panels to track the movement of the sun from East toWest, wherein said control system makes use of pre-programmedinformation including but not limited to the date, a suitable time clockstandard, and sun position information which includes at least onestarting point input provided after system installation, as well as sunposition data such as can be readily obtained from solar ephemeris data.13. The method for tracking the position of the sun according to claim12, wherein said tracking system does not utilize any type of solarenergy sensing device.
 14. The method for tracking the position of thesun according to claim 12, wherein said tracking system makes use ofordinary photocells only for the purpose of detecting sunrise, sunset orsufficiently bad or overcast weather to justify returning said rotatingsolar panels to the flat position with respect to the solar moduleframework.
 15. The method for tracking the position of the sun accordingto claim 12, wherein said rotating solar panels are capable of rotatingat least about +/−60 degrees from the flat position with respect to thesolar module framework.
 16. The method for tracking the position of thesun according to claim 12, wherein said tracking system is calibrated byentering at least one and preferably two sun position versus time of daydata points into said control system program at different hours of theday, each said sun position defined as the panel rotation angle thatmaximizes solar energy capture at a particular time of day.
 17. Themethod for tracking the position of the sun according to claim 12,wherein said reversible electric motor is a gearmotor driving a piniongear which engages a linear rack gear, said linear rack gear beingsupported and captured by suitable flanged roller bearings which insureproper contact with pinion gears which are mounted on the longitudinalaxes of said one or more rotating solar panels.
 18. The method fortracking the position of the sun according to claim 12, wherein saidrotating solar panels are mounted parallel to one another inside amodular framework.
 19. The method of mounting solar panels according toclaim 18, wherein said modular framework is low-profile, less than about6 inches high, and suited for mounting on almost any type of roof orstructure, including but not limited to gazebos, patios, greenhouses,garages, residential homes, commercial buildings, shopping centers,sports arenas, open ground, or military installations such as aircrafthangers or ships.
 20. The method for tracking the position of the sunaccording to claim 12, wherein said tracking system is programmed toreturn said one or more solar panels after sunset from the end of dayWesternmost pointing direction to the start of day Easternmostdirection, so as to be ready for solar tracking again before sunrise onthe next day.
 21. The method for tracking the position of the sunaccording to claim 12, wherein said tracking system is programmed toreturn said one or more solar panels to the flat or pointed upwardsposition which is parallel with the modular framework whenever the solarenergy capture during daylight hours falls below a predeterminedthreshold, thereby indicating cloudy or overcast sky conditions.
 22. Themethod for tracking the position of the sun according to claim 12,wherein the control system program is simplified by assuming that allinstallations are located at the same latitude, for example, in theUnited States, at about 40 degrees North latitude.